Data.Colour.RGB:hslsv from colour-2.3.3, B

Percentage Accurate: 99.2% → 99.8%

Time: 13.1s

Alternatives: 17

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((60.0d0 * (x - y)) / (z - t)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 * (x - y)) / (z - t)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 * Float64(x - y)) / Float64(z - t)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 * (x - y)) / (z - t)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(a, 120, \frac{60}{z - t} \cdot \left(x - y\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (fma a 120.0 (* (/ 60.0 (- z t)) (- x y))))

C

double code(double x, double y, double z, double t, double a) {
	return fma(a, 120.0, ((60.0 / (z - t)) * (x - y)));
}

Julia

function code(x, y, z, t, a)
	return fma(a, 120.0, Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y)))
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0 + N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. +-commutative 99.4%

      \[\leadsto \color{blue}{a \cdot 120 + \frac{60 \cdot \left(x - y\right)}{z - t}} \]

   2. fma-def 99.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60 \cdot \left(x - y\right)}{z - t}\right)} \]

   3. associate-*l/ 99.8%

      \[\leadsto \mathsf{fma}\left(a, 120, \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)}\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, 120, \frac{60}{z - t} \cdot \left(x - y\right)\right)} \]

4. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(a, 120, \frac{60}{z - t} \cdot \left(x - y\right)\right) \]

Alternative 2: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(60, \frac{x - y}{z - t}, a \cdot 120\right) \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (fma 60.0 (/ (- x y) (- z t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return fma(60.0, ((x - y) / (z - t)), (a * 120.0));
}

Julia

function code(x, y, z, t, a)
	return fma(60.0, Float64(Float64(x - y) / Float64(z - t)), Float64(a * 120.0))
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. associate-*r/ 99.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} + a \cdot 120 \]

   2. fma-def 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x - y}{z - t}, a \cdot 120\right)} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(60, \frac{x - y}{z - t}, a \cdot 120\right)} \]

4. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(60, \frac{x - y}{z - t}, a \cdot 120\right) \]

Alternative 3: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x - y}{z - t}\\ \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+82}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -15000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-42}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ (- x y) (- z t)))))
   (if (<= (* a 120.0) -5e+82)
     (* a 120.0)
     (if (<= (* a 120.0) -15000000000000.0)
       t_1
       (if (<= (* a 120.0) -4e-42)
         (+ (* a 120.0) (* y (/ -60.0 z)))
         (if (<= (* a 120.0) 5e-64) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -5e+82) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -15000000000000.0) {
		tmp = t_1;
	} else if ((a * 120.0) <= -4e-42) {
		tmp = (a * 120.0) + (y * (-60.0 / z));
	} else if ((a * 120.0) <= 5e-64) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * ((x - y) / (z - t))
    if ((a * 120.0d0) <= (-5d+82)) then
        tmp = a * 120.0d0
    else if ((a * 120.0d0) <= (-15000000000000.0d0)) then
        tmp = t_1
    else if ((a * 120.0d0) <= (-4d-42)) then
        tmp = (a * 120.0d0) + (y * ((-60.0d0) / z))
    else if ((a * 120.0d0) <= 5d-64) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * ((x - y) / (z - t));
	double tmp;
	if ((a * 120.0) <= -5e+82) {
		tmp = a * 120.0;
	} else if ((a * 120.0) <= -15000000000000.0) {
		tmp = t_1;
	} else if ((a * 120.0) <= -4e-42) {
		tmp = (a * 120.0) + (y * (-60.0 / z));
	} else if ((a * 120.0) <= 5e-64) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * ((x - y) / (z - t))
	tmp = 0
	if (a * 120.0) <= -5e+82:
		tmp = a * 120.0
	elif (a * 120.0) <= -15000000000000.0:
		tmp = t_1
	elif (a * 120.0) <= -4e-42:
		tmp = (a * 120.0) + (y * (-60.0 / z))
	elif (a * 120.0) <= 5e-64:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)))
	tmp = 0.0
	if (Float64(a * 120.0) <= -5e+82)
		tmp = Float64(a * 120.0);
	elseif (Float64(a * 120.0) <= -15000000000000.0)
		tmp = t_1;
	elseif (Float64(a * 120.0) <= -4e-42)
		tmp = Float64(Float64(a * 120.0) + Float64(y * Float64(-60.0 / z)));
	elseif (Float64(a * 120.0) <= 5e-64)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * ((x - y) / (z - t));
	tmp = 0.0;
	if ((a * 120.0) <= -5e+82)
		tmp = a * 120.0;
	elseif ((a * 120.0) <= -15000000000000.0)
		tmp = t_1;
	elseif ((a * 120.0) <= -4e-42)
		tmp = (a * 120.0) + (y * (-60.0 / z));
	elseif ((a * 120.0) <= 5e-64)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * 120.0), $MachinePrecision], -5e+82], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], -15000000000000.0], t$95$1, If[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-42], N[(N[(a * 120.0), $MachinePrecision] + N[(y * N[(-60.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(a * 120.0), $MachinePrecision], 5e-64], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 a 120) < -5.00000000000000015e82 or 5.00000000000000033e-64 < (*.f64 a 120)

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 83.9%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -5.00000000000000015e82 < (*.f64 a 120) < -1.5e13 or -4.00000000000000015e-42 < (*.f64 a 120) < 5.00000000000000033e-64

   1. Initial program 98.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in a around 0 78.0%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]

   if -1.5e13 < (*.f64 a 120) < -4.00000000000000015e-42

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/r/ 100.0%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   5. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   6. Taylor expanded in z around inf 88.5%

      \[\leadsto \color{blue}{\frac{60}{z}} \cdot \left(x - y\right) + a \cdot 120 \]

   7. Taylor expanded in x around 0 81.2%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z}} + a \cdot 120 \]
   8. Step-by-step derivation

      1. associate-*r/ 81.2%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z}} + a \cdot 120 \]

      2. *-commutative 81.2%

         \[\leadsto \frac{\color{blue}{y \cdot -60}}{z} + a \cdot 120 \]

      3. associate-/l* 81.2%

         \[\leadsto \color{blue}{\frac{y}{\frac{z}{-60}}} + a \cdot 120 \]

   9. Simplified 81.2%

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{-60}}} + a \cdot 120 \]
   10. Step-by-step derivation

       1. div-inv 81.2%

          \[\leadsto \color{blue}{y \cdot \frac{1}{\frac{z}{-60}}} + a \cdot 120 \]

       2. clear-num 81.2%

          \[\leadsto y \cdot \color{blue}{\frac{-60}{z}} + a \cdot 120 \]

   11. Applied egg-rr 81.2%

       \[\leadsto \color{blue}{y \cdot \frac{-60}{z}} + a \cdot 120 \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -5 \cdot 10^{+82}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \cdot 120 \leq -15000000000000:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{elif}\;a \cdot 120 \leq -4 \cdot 10^{-42}:\\ \;\;\;\;a \cdot 120 + y \cdot \frac{-60}{z}\\ \mathbf{elif}\;a \cdot 120 \leq 5 \cdot 10^{-64}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 4: 54.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 60 \cdot \frac{x}{z - t}\\ \mathbf{if}\;z - t \leq -2 \cdot 10^{+69}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq -5 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z - t \leq -1 \cdot 10^{-186}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;z - t \leq 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* 60.0 (/ x (- z t)))))
   (if (<= (- z t) -2e+69)
     (* a 120.0)
     (if (<= (- z t) -5e-65)
       t_1
       (if (<= (- z t) -1e-186)
         (* -60.0 (/ y (- z t)))
         (if (<= (- z t) 1e-31) t_1 (* a 120.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double tmp;
	if ((z - t) <= -2e+69) {
		tmp = a * 120.0;
	} else if ((z - t) <= -5e-65) {
		tmp = t_1;
	} else if ((z - t) <= -1e-186) {
		tmp = -60.0 * (y / (z - t));
	} else if ((z - t) <= 1e-31) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 60.0d0 * (x / (z - t))
    if ((z - t) <= (-2d+69)) then
        tmp = a * 120.0d0
    else if ((z - t) <= (-5d-65)) then
        tmp = t_1
    else if ((z - t) <= (-1d-186)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if ((z - t) <= 1d-31) then
        tmp = t_1
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = 60.0 * (x / (z - t));
	double tmp;
	if ((z - t) <= -2e+69) {
		tmp = a * 120.0;
	} else if ((z - t) <= -5e-65) {
		tmp = t_1;
	} else if ((z - t) <= -1e-186) {
		tmp = -60.0 * (y / (z - t));
	} else if ((z - t) <= 1e-31) {
		tmp = t_1;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = 60.0 * (x / (z - t))
	tmp = 0
	if (z - t) <= -2e+69:
		tmp = a * 120.0
	elif (z - t) <= -5e-65:
		tmp = t_1
	elif (z - t) <= -1e-186:
		tmp = -60.0 * (y / (z - t))
	elif (z - t) <= 1e-31:
		tmp = t_1
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(60.0 * Float64(x / Float64(z - t)))
	tmp = 0.0
	if (Float64(z - t) <= -2e+69)
		tmp = Float64(a * 120.0);
	elseif (Float64(z - t) <= -5e-65)
		tmp = t_1;
	elseif (Float64(z - t) <= -1e-186)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (Float64(z - t) <= 1e-31)
		tmp = t_1;
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = 60.0 * (x / (z - t));
	tmp = 0.0;
	if ((z - t) <= -2e+69)
		tmp = a * 120.0;
	elseif ((z - t) <= -5e-65)
		tmp = t_1;
	elseif ((z - t) <= -1e-186)
		tmp = -60.0 * (y / (z - t));
	elseif ((z - t) <= 1e-31)
		tmp = t_1;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z - t), $MachinePrecision], -2e+69], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], -5e-65], t$95$1, If[LessEqual[N[(z - t), $MachinePrecision], -1e-186], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 1e-31], t$95$1, N[(a * 120.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 z t) < -2.0000000000000001e69 or 1e-31 < (-.f64 z t)

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 65.5%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -2.0000000000000001e69 < (-.f64 z t) < -4.99999999999999983e-65 or -9.9999999999999991e-187 < (-.f64 z t) < 1e-31

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/r/ 99.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   6. Taylor expanded in x around inf 58.8%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]

   if -4.99999999999999983e-65 < (-.f64 z t) < -9.9999999999999991e-187

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/r/ 99.6%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   6. Taylor expanded in y around inf 82.3%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -2 \cdot 10^{+69}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq -5 \cdot 10^{-65}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{elif}\;z - t \leq -1 \cdot 10^{-186}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;z - t \leq 10^{-31}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 5: 54.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -2 \cdot 10^{+69}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq -5 \cdot 10^{-65}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;z - t \leq -1 \cdot 10^{-186}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;z - t \leq 10^{-31}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- z t) -2e+69)
   (* a 120.0)
   (if (<= (- z t) -5e-65)
     (/ 60.0 (/ (- z t) x))
     (if (<= (- z t) -1e-186)
       (* -60.0 (/ y (- z t)))
       (if (<= (- z t) 1e-31) (* 60.0 (/ x (- z t))) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -2e+69) {
		tmp = a * 120.0;
	} else if ((z - t) <= -5e-65) {
		tmp = 60.0 / ((z - t) / x);
	} else if ((z - t) <= -1e-186) {
		tmp = -60.0 * (y / (z - t));
	} else if ((z - t) <= 1e-31) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z - t) <= (-2d+69)) then
        tmp = a * 120.0d0
    else if ((z - t) <= (-5d-65)) then
        tmp = 60.0d0 / ((z - t) / x)
    else if ((z - t) <= (-1d-186)) then
        tmp = (-60.0d0) * (y / (z - t))
    else if ((z - t) <= 1d-31) then
        tmp = 60.0d0 * (x / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -2e+69) {
		tmp = a * 120.0;
	} else if ((z - t) <= -5e-65) {
		tmp = 60.0 / ((z - t) / x);
	} else if ((z - t) <= -1e-186) {
		tmp = -60.0 * (y / (z - t));
	} else if ((z - t) <= 1e-31) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) <= -2e+69:
		tmp = a * 120.0
	elif (z - t) <= -5e-65:
		tmp = 60.0 / ((z - t) / x)
	elif (z - t) <= -1e-186:
		tmp = -60.0 * (y / (z - t))
	elif (z - t) <= 1e-31:
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z - t) <= -2e+69)
		tmp = Float64(a * 120.0);
	elseif (Float64(z - t) <= -5e-65)
		tmp = Float64(60.0 / Float64(Float64(z - t) / x));
	elseif (Float64(z - t) <= -1e-186)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	elseif (Float64(z - t) <= 1e-31)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z - t) <= -2e+69)
		tmp = a * 120.0;
	elseif ((z - t) <= -5e-65)
		tmp = 60.0 / ((z - t) / x);
	elseif ((z - t) <= -1e-186)
		tmp = -60.0 * (y / (z - t));
	elseif ((z - t) <= 1e-31)
		tmp = 60.0 * (x / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z - t), $MachinePrecision], -2e+69], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], -5e-65], N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], -1e-186], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 1e-31], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 z t) < -2.0000000000000001e69 or 1e-31 < (-.f64 z t)

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 65.5%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -2.0000000000000001e69 < (-.f64 z t) < -4.99999999999999983e-65

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/r/ 99.9%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   6. Taylor expanded in x around inf 54.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   7. Step-by-step derivation

      1. associate-*r/ 54.1%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

      2. *-commutative 54.1%

         \[\leadsto \frac{\color{blue}{x \cdot 60}}{z - t} \]

   8. Simplified 54.1%

      \[\leadsto \color{blue}{\frac{x \cdot 60}{z - t}} \]

   9. Taylor expanded in x around 0 54.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   10. Step-by-step derivation

       1. associate-*r/ 54.1%

          \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

       2. associate-/l* 54.1%

          \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x}}} \]

   11. Simplified 54.1%

       \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x}}} \]

   if -4.99999999999999983e-65 < (-.f64 z t) < -9.9999999999999991e-187

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/r/ 99.6%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   6. Taylor expanded in y around inf 82.3%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]

   if -9.9999999999999991e-187 < (-.f64 z t) < 1e-31

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/r/ 99.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   6. Taylor expanded in x around inf 61.5%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -2 \cdot 10^{+69}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq -5 \cdot 10^{-65}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;z - t \leq -1 \cdot 10^{-186}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{elif}\;z - t \leq 10^{-31}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 6: 54.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -2 \cdot 10^{+69}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq -5 \cdot 10^{-65}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;z - t \leq -1 \cdot 10^{-186}:\\ \;\;\;\;\frac{y}{\frac{z - t}{-60}}\\ \mathbf{elif}\;z - t \leq 10^{-31}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (- z t) -2e+69)
   (* a 120.0)
   (if (<= (- z t) -5e-65)
     (/ 60.0 (/ (- z t) x))
     (if (<= (- z t) -1e-186)
       (/ y (/ (- z t) -60.0))
       (if (<= (- z t) 1e-31) (* 60.0 (/ x (- z t))) (* a 120.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -2e+69) {
		tmp = a * 120.0;
	} else if ((z - t) <= -5e-65) {
		tmp = 60.0 / ((z - t) / x);
	} else if ((z - t) <= -1e-186) {
		tmp = y / ((z - t) / -60.0);
	} else if ((z - t) <= 1e-31) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z - t) <= (-2d+69)) then
        tmp = a * 120.0d0
    else if ((z - t) <= (-5d-65)) then
        tmp = 60.0d0 / ((z - t) / x)
    else if ((z - t) <= (-1d-186)) then
        tmp = y / ((z - t) / (-60.0d0))
    else if ((z - t) <= 1d-31) then
        tmp = 60.0d0 * (x / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z - t) <= -2e+69) {
		tmp = a * 120.0;
	} else if ((z - t) <= -5e-65) {
		tmp = 60.0 / ((z - t) / x);
	} else if ((z - t) <= -1e-186) {
		tmp = y / ((z - t) / -60.0);
	} else if ((z - t) <= 1e-31) {
		tmp = 60.0 * (x / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z - t) <= -2e+69:
		tmp = a * 120.0
	elif (z - t) <= -5e-65:
		tmp = 60.0 / ((z - t) / x)
	elif (z - t) <= -1e-186:
		tmp = y / ((z - t) / -60.0)
	elif (z - t) <= 1e-31:
		tmp = 60.0 * (x / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z - t) <= -2e+69)
		tmp = Float64(a * 120.0);
	elseif (Float64(z - t) <= -5e-65)
		tmp = Float64(60.0 / Float64(Float64(z - t) / x));
	elseif (Float64(z - t) <= -1e-186)
		tmp = Float64(y / Float64(Float64(z - t) / -60.0));
	elseif (Float64(z - t) <= 1e-31)
		tmp = Float64(60.0 * Float64(x / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z - t) <= -2e+69)
		tmp = a * 120.0;
	elseif ((z - t) <= -5e-65)
		tmp = 60.0 / ((z - t) / x);
	elseif ((z - t) <= -1e-186)
		tmp = y / ((z - t) / -60.0);
	elseif ((z - t) <= 1e-31)
		tmp = 60.0 * (x / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z - t), $MachinePrecision], -2e+69], N[(a * 120.0), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], -5e-65], N[(60.0 / N[(N[(z - t), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], -1e-186], N[(y / N[(N[(z - t), $MachinePrecision] / -60.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z - t), $MachinePrecision], 1e-31], N[(60.0 * N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 z t) < -2.0000000000000001e69 or 1e-31 < (-.f64 z t)

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 65.5%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -2.0000000000000001e69 < (-.f64 z t) < -4.99999999999999983e-65

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/r/ 99.9%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   6. Taylor expanded in x around inf 54.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   7. Step-by-step derivation

      1. associate-*r/ 54.1%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

      2. *-commutative 54.1%

         \[\leadsto \frac{\color{blue}{x \cdot 60}}{z - t} \]

   8. Simplified 54.1%

      \[\leadsto \color{blue}{\frac{x \cdot 60}{z - t}} \]

   9. Taylor expanded in x around 0 54.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   10. Step-by-step derivation

       1. associate-*r/ 54.1%

          \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

       2. associate-/l* 54.1%

          \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x}}} \]

   11. Simplified 54.1%

       \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x}}} \]

   if -4.99999999999999983e-65 < (-.f64 z t) < -9.9999999999999991e-187

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/r/ 99.6%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   6. Taylor expanded in a around 0 99.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   7. Step-by-step derivation

      1. *-commutative 99.7%

         \[\leadsto \color{blue}{\frac{x - y}{z - t} \cdot 60} \]

      2. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 60}{z - t}} \]

   8. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 60}{z - t}} \]

   9. Taylor expanded in x around 0 82.3%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
   10. Step-by-step derivation

       1. associate-*r/ 82.4%

          \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} \]

       2. *-commutative 82.4%

          \[\leadsto \frac{\color{blue}{y \cdot -60}}{z - t} \]

       3. associate-/l* 82.4%

          \[\leadsto \color{blue}{\frac{y}{\frac{z - t}{-60}}} \]

   11. Simplified 82.4%

       \[\leadsto \color{blue}{\frac{y}{\frac{z - t}{-60}}} \]

   if -9.9999999999999991e-187 < (-.f64 z t) < 1e-31

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/r/ 99.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   6. Taylor expanded in x around inf 61.5%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -2 \cdot 10^{+69}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;z - t \leq -5 \cdot 10^{-65}:\\ \;\;\;\;\frac{60}{\frac{z - t}{x}}\\ \mathbf{elif}\;z - t \leq -1 \cdot 10^{-186}:\\ \;\;\;\;\frac{y}{\frac{z - t}{-60}}\\ \mathbf{elif}\;z - t \leq 10^{-31}:\\ \;\;\;\;60 \cdot \frac{x}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 7: 53.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -60 \cdot \frac{x}{t}\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{+18}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-47}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-172}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-159}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -60.0 (/ x t))))
   (if (<= a -1.55e+61)
     (* a 120.0)
     (if (<= a -3.3e+18)
       (/ (* 60.0 y) t)
       (if (<= a -1.3e-47)
         (* a 120.0)
         (if (<= a -4.7e-101)
           t_1
           (if (<= a -5.6e-172)
             (* a 120.0)
             (if (<= a -2.2e-251)
               t_1
               (if (<= a 1.45e-159)
                 (* -60.0 (/ y (- z t)))
                 (* a 120.0))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / t);
	double tmp;
	if (a <= -1.55e+61) {
		tmp = a * 120.0;
	} else if (a <= -3.3e+18) {
		tmp = (60.0 * y) / t;
	} else if (a <= -1.3e-47) {
		tmp = a * 120.0;
	} else if (a <= -4.7e-101) {
		tmp = t_1;
	} else if (a <= -5.6e-172) {
		tmp = a * 120.0;
	} else if (a <= -2.2e-251) {
		tmp = t_1;
	} else if (a <= 1.45e-159) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-60.0d0) * (x / t)
    if (a <= (-1.55d+61)) then
        tmp = a * 120.0d0
    else if (a <= (-3.3d+18)) then
        tmp = (60.0d0 * y) / t
    else if (a <= (-1.3d-47)) then
        tmp = a * 120.0d0
    else if (a <= (-4.7d-101)) then
        tmp = t_1
    else if (a <= (-5.6d-172)) then
        tmp = a * 120.0d0
    else if (a <= (-2.2d-251)) then
        tmp = t_1
    else if (a <= 1.45d-159) then
        tmp = (-60.0d0) * (y / (z - t))
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -60.0 * (x / t);
	double tmp;
	if (a <= -1.55e+61) {
		tmp = a * 120.0;
	} else if (a <= -3.3e+18) {
		tmp = (60.0 * y) / t;
	} else if (a <= -1.3e-47) {
		tmp = a * 120.0;
	} else if (a <= -4.7e-101) {
		tmp = t_1;
	} else if (a <= -5.6e-172) {
		tmp = a * 120.0;
	} else if (a <= -2.2e-251) {
		tmp = t_1;
	} else if (a <= 1.45e-159) {
		tmp = -60.0 * (y / (z - t));
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -60.0 * (x / t)
	tmp = 0
	if a <= -1.55e+61:
		tmp = a * 120.0
	elif a <= -3.3e+18:
		tmp = (60.0 * y) / t
	elif a <= -1.3e-47:
		tmp = a * 120.0
	elif a <= -4.7e-101:
		tmp = t_1
	elif a <= -5.6e-172:
		tmp = a * 120.0
	elif a <= -2.2e-251:
		tmp = t_1
	elif a <= 1.45e-159:
		tmp = -60.0 * (y / (z - t))
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-60.0 * Float64(x / t))
	tmp = 0.0
	if (a <= -1.55e+61)
		tmp = Float64(a * 120.0);
	elseif (a <= -3.3e+18)
		tmp = Float64(Float64(60.0 * y) / t);
	elseif (a <= -1.3e-47)
		tmp = Float64(a * 120.0);
	elseif (a <= -4.7e-101)
		tmp = t_1;
	elseif (a <= -5.6e-172)
		tmp = Float64(a * 120.0);
	elseif (a <= -2.2e-251)
		tmp = t_1;
	elseif (a <= 1.45e-159)
		tmp = Float64(-60.0 * Float64(y / Float64(z - t)));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -60.0 * (x / t);
	tmp = 0.0;
	if (a <= -1.55e+61)
		tmp = a * 120.0;
	elseif (a <= -3.3e+18)
		tmp = (60.0 * y) / t;
	elseif (a <= -1.3e-47)
		tmp = a * 120.0;
	elseif (a <= -4.7e-101)
		tmp = t_1;
	elseif (a <= -5.6e-172)
		tmp = a * 120.0;
	elseif (a <= -2.2e-251)
		tmp = t_1;
	elseif (a <= 1.45e-159)
		tmp = -60.0 * (y / (z - t));
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.55e+61], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -3.3e+18], N[(N[(60.0 * y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, -1.3e-47], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -4.7e-101], t$95$1, If[LessEqual[a, -5.6e-172], N[(a * 120.0), $MachinePrecision], If[LessEqual[a, -2.2e-251], t$95$1, If[LessEqual[a, 1.45e-159], N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.55e61 or -3.3e18 < a < -1.3e-47 or -4.6999999999999999e-101 < a < -5.60000000000000023e-172 or 1.44999999999999995e-159 < a

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 71.3%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -1.55e61 < a < -3.3e18

   1. Initial program 100.0%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/r/ 99.8%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   6. Taylor expanded in a around 0 85.7%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   7. Step-by-step derivation

      1. *-commutative 85.7%

         \[\leadsto \color{blue}{\frac{x - y}{z - t} \cdot 60} \]

      2. associate-*l/ 85.9%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 60}{z - t}} \]

   8. Simplified 85.9%

      \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 60}{z - t}} \]

   9. Taylor expanded in z around 0 86.5%

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t}} \]
   10. Step-by-step derivation

       1. associate-*r/ 86.7%

          \[\leadsto \color{blue}{\frac{-60 \cdot \left(x - y\right)}{t}} \]

       2. *-commutative 86.7%

          \[\leadsto \frac{\color{blue}{\left(x - y\right) \cdot -60}}{t} \]

   11. Simplified 86.7%

       \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot -60}{t}} \]

   12. Taylor expanded in x around 0 72.9%

       \[\leadsto \frac{\color{blue}{60 \cdot y}}{t} \]
   13. Step-by-step derivation

       1. *-commutative 72.9%

          \[\leadsto \frac{\color{blue}{y \cdot 60}}{t} \]

   14. Simplified 72.9%

       \[\leadsto \frac{\color{blue}{y \cdot 60}}{t} \]

   if -1.3e-47 < a < -4.6999999999999999e-101 or -5.60000000000000023e-172 < a < -2.2e-251

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/r/ 99.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   6. Taylor expanded in x around inf 67.1%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   7. Step-by-step derivation

      1. associate-*r/ 67.1%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

      2. *-commutative 67.1%

         \[\leadsto \frac{\color{blue}{x \cdot 60}}{z - t} \]

   8. Simplified 67.1%

      \[\leadsto \color{blue}{\frac{x \cdot 60}{z - t}} \]

   9. Taylor expanded in z around 0 56.5%

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t}} \]

   if -2.2e-251 < a < 1.44999999999999995e-159

   1. Initial program 99.6%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/r/ 99.5%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   6. Taylor expanded in y around inf 54.7%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.55 \cdot 10^{+61}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{+18}:\\ \;\;\;\;\frac{60 \cdot y}{t}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-47}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -4.7 \cdot 10^{-101}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-172}:\\ \;\;\;\;a \cdot 120\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-251}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-159}:\\ \;\;\;\;-60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 8: 82.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-42} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-102}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* a 120.0) -4e-42) (not (<= (* a 120.0) 2e-102)))
   (+ (* a 120.0) (* -60.0 (/ y (- z t))))
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -4e-42) || !((a * 120.0) <= 2e-102)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((a * 120.0d0) <= (-4d-42)) .or. (.not. ((a * 120.0d0) <= 2d-102))) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((a * 120.0) <= -4e-42) || !((a * 120.0) <= 2e-102)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((a * 120.0) <= -4e-42) or not ((a * 120.0) <= 2e-102):
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(a * 120.0) <= -4e-42) || !(Float64(a * 120.0) <= 2e-102))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((a * 120.0) <= -4e-42) || ~(((a * 120.0) <= 2e-102)))
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(a * 120.0), $MachinePrecision], -4e-42], N[Not[LessEqual[N[(a * 120.0), $MachinePrecision], 2e-102]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 a 120) < -4.00000000000000015e-42 or 1.99999999999999987e-102 < (*.f64 a 120)

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in x around 0 88.1%

      \[\leadsto \color{blue}{120 \cdot a + -60 \cdot \frac{y}{z - t}} \]

   if -4.00000000000000015e-42 < (*.f64 a 120) < 1.99999999999999987e-102

   1. Initial program 98.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in a around 0 80.0%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \cdot 120 \leq -4 \cdot 10^{-42} \lor \neg \left(a \cdot 120 \leq 2 \cdot 10^{-102}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 9: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+79} \lor \neg \left(a \leq -100000000000\right) \land \left(a \leq -1 \cdot 10^{-44} \lor \neg \left(a \leq 7.4 \cdot 10^{-59}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.15e+79)
         (and (not (<= a -100000000000.0))
              (or (<= a -1e-44) (not (<= a 7.4e-59)))))
   (* a 120.0)
   (* 60.0 (/ (- x y) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.15e+79) || (!(a <= -100000000000.0) && ((a <= -1e-44) || !(a <= 7.4e-59)))) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.15d+79)) .or. (.not. (a <= (-100000000000.0d0))) .and. (a <= (-1d-44)) .or. (.not. (a <= 7.4d-59))) then
        tmp = a * 120.0d0
    else
        tmp = 60.0d0 * ((x - y) / (z - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.15e+79) || (!(a <= -100000000000.0) && ((a <= -1e-44) || !(a <= 7.4e-59)))) {
		tmp = a * 120.0;
	} else {
		tmp = 60.0 * ((x - y) / (z - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.15e+79) or (not (a <= -100000000000.0) and ((a <= -1e-44) or not (a <= 7.4e-59))):
		tmp = a * 120.0
	else:
		tmp = 60.0 * ((x - y) / (z - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.15e+79) || (!(a <= -100000000000.0) && ((a <= -1e-44) || !(a <= 7.4e-59))))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(60.0 * Float64(Float64(x - y) / Float64(z - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.15e+79) || (~((a <= -100000000000.0)) && ((a <= -1e-44) || ~((a <= 7.4e-59)))))
		tmp = a * 120.0;
	else
		tmp = 60.0 * ((x - y) / (z - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.15e+79], And[N[Not[LessEqual[a, -100000000000.0]], $MachinePrecision], Or[LessEqual[a, -1e-44], N[Not[LessEqual[a, 7.4e-59]], $MachinePrecision]]]], N[(a * 120.0), $MachinePrecision], N[(60.0 * N[(N[(x - y), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.15e79 or -1e11 < a < -9.99999999999999953e-45 or 7.3999999999999998e-59 < a

   1. Initial program 99.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 82.1%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -1.15e79 < a < -1e11 or -9.99999999999999953e-45 < a < 7.3999999999999998e-59

   1. Initial program 98.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in a around 0 78.0%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+79} \lor \neg \left(a \leq -100000000000\right) \land \left(a \leq -1 \cdot 10^{-44} \lor \neg \left(a \leq 7.4 \cdot 10^{-59}\right)\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;60 \cdot \frac{x - y}{z - t}\\ \end{array} \]

Alternative 10: 55.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -1 \cdot 10^{+70} \lor \neg \left(z - t \leq 10^{-60}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- z t) -1e+70) (not (<= (- z t) 1e-60)))
   (* a 120.0)
   (* -60.0 (/ (- x y) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) <= -1e+70) || !((z - t) <= 1e-60)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((z - t) <= (-1d+70)) .or. (.not. ((z - t) <= 1d-60))) then
        tmp = a * 120.0d0
    else
        tmp = (-60.0d0) * ((x - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) <= -1e+70) || !((z - t) <= 1e-60)) {
		tmp = a * 120.0;
	} else {
		tmp = -60.0 * ((x - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((z - t) <= -1e+70) or not ((z - t) <= 1e-60):
		tmp = a * 120.0
	else:
		tmp = -60.0 * ((x - y) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(z - t) <= -1e+70) || !(Float64(z - t) <= 1e-60))
		tmp = Float64(a * 120.0);
	else
		tmp = Float64(-60.0 * Float64(Float64(x - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z - t) <= -1e+70) || ~(((z - t) <= 1e-60)))
		tmp = a * 120.0;
	else
		tmp = -60.0 * ((x - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(z - t), $MachinePrecision], -1e+70], N[Not[LessEqual[N[(z - t), $MachinePrecision], 1e-60]], $MachinePrecision]], N[(a * 120.0), $MachinePrecision], N[(-60.0 * N[(N[(x - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -1.00000000000000007e70 or 9.9999999999999997e-61 < (-.f64 z t)

   1. Initial program 99.3%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 64.9%

      \[\leadsto \color{blue}{120 \cdot a} \]

   if -1.00000000000000007e70 < (-.f64 z t) < 9.9999999999999997e-61

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/r/ 99.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   6. Taylor expanded in a around 0 82.9%

      \[\leadsto \color{blue}{60 \cdot \frac{x - y}{z - t}} \]
   7. Step-by-step derivation

      1. *-commutative 82.9%

         \[\leadsto \color{blue}{\frac{x - y}{z - t} \cdot 60} \]

      2. associate-*l/ 82.9%

         \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 60}{z - t}} \]

   8. Simplified 82.9%

      \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot 60}{z - t}} \]

   9. Taylor expanded in z around 0 54.1%

      \[\leadsto \color{blue}{-60 \cdot \frac{x - y}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -1 \cdot 10^{+70} \lor \neg \left(z - t \leq 10^{-60}\right):\\ \;\;\;\;a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;-60 \cdot \frac{x - y}{t}\\ \end{array} \]

Alternative 11: 89.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+69} \lor \neg \left(y \leq 6 \cdot 10^{+28}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.2e+69) (not (<= y 6e+28)))
   (+ (* a 120.0) (* -60.0 (/ y (- z t))))
   (+ (* (/ 60.0 (- z t)) x) (* a 120.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.2e+69) || !(y <= 6e+28)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.2d+69)) .or. (.not. (y <= 6d+28))) then
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    else
        tmp = ((60.0d0 / (z - t)) * x) + (a * 120.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.2e+69) || !(y <= 6e+28)) {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	} else {
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.2e+69) or not (y <= 6e+28):
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	else:
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.2e+69) || !(y <= 6e+28))
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	else
		tmp = Float64(Float64(Float64(60.0 / Float64(z - t)) * x) + Float64(a * 120.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.2e+69) || ~((y <= 6e+28)))
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	else
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.2e+69], N[Not[LessEqual[y, 6e+28]], $MachinePrecision]], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2000000000000001e69 or 6.0000000000000002e28 < y

   1. Initial program 98.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in x around 0 88.4%

      \[\leadsto \color{blue}{120 \cdot a + -60 \cdot \frac{y}{z - t}} \]

   if -1.2000000000000001e69 < y < 6.0000000000000002e28

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in x around inf 95.0%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. associate-*r/ 95.0%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} + a \cdot 120 \]

      2. associate-*l/ 95.0%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot x} + a \cdot 120 \]

      3. *-commutative 95.0%

         \[\leadsto \color{blue}{x \cdot \frac{60}{z - t}} + a \cdot 120 \]

   6. Simplified 95.0%

      \[\leadsto \color{blue}{x \cdot \frac{60}{z - t}} + a \cdot 120 \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+69} \lor \neg \left(y \leq 6 \cdot 10^{+28}\right):\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \end{array} \]

Alternative 12: 89.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+65}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{elif}\;y \leq 3.95 \cdot 10^{+30}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.9e+65)
   (+ (/ -60.0 (/ (- z t) y)) (* a 120.0))
   (if (<= y 3.95e+30)
     (+ (* (/ 60.0 (- z t)) x) (* a 120.0))
     (+ (* a 120.0) (* -60.0 (/ y (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.9e+65) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else if (y <= 3.95e+30) {
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.9d+65)) then
        tmp = ((-60.0d0) / ((z - t) / y)) + (a * 120.0d0)
    else if (y <= 3.95d+30) then
        tmp = ((60.0d0 / (z - t)) * x) + (a * 120.0d0)
    else
        tmp = (a * 120.0d0) + ((-60.0d0) * (y / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.9e+65) {
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	} else if (y <= 3.95e+30) {
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	} else {
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.9e+65:
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0)
	elif y <= 3.95e+30:
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0)
	else:
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.9e+65)
		tmp = Float64(Float64(-60.0 / Float64(Float64(z - t) / y)) + Float64(a * 120.0));
	elseif (y <= 3.95e+30)
		tmp = Float64(Float64(Float64(60.0 / Float64(z - t)) * x) + Float64(a * 120.0));
	else
		tmp = Float64(Float64(a * 120.0) + Float64(-60.0 * Float64(y / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.9e+65)
		tmp = (-60.0 / ((z - t) / y)) + (a * 120.0);
	elseif (y <= 3.95e+30)
		tmp = ((60.0 / (z - t)) * x) + (a * 120.0);
	else
		tmp = (a * 120.0) + (-60.0 * (y / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.9e+65], N[(N[(-60.0 / N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.95e+30], N[(N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision], N[(N[(a * 120.0), $MachinePrecision] + N[(-60.0 * N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9e65

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in x around 0 88.0%

      \[\leadsto \color{blue}{-60 \cdot \frac{y}{z - t}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. associate-*r/ 88.0%

         \[\leadsto \color{blue}{\frac{-60 \cdot y}{z - t}} + a \cdot 120 \]

      2. associate-/l* 88.0%

         \[\leadsto \color{blue}{\frac{-60}{\frac{z - t}{y}}} + a \cdot 120 \]

   6. Simplified 88.0%

      \[\leadsto \color{blue}{\frac{-60}{\frac{z - t}{y}}} + a \cdot 120 \]

   if -2.9e65 < y < 3.94999999999999981e30

   1. Initial program 99.8%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in x around inf 95.0%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} + a \cdot 120 \]
   5. Step-by-step derivation

      1. associate-*r/ 95.0%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} + a \cdot 120 \]

      2. associate-*l/ 95.0%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot x} + a \cdot 120 \]

      3. *-commutative 95.0%

         \[\leadsto \color{blue}{x \cdot \frac{60}{z - t}} + a \cdot 120 \]

   6. Simplified 95.0%

      \[\leadsto \color{blue}{x \cdot \frac{60}{z - t}} + a \cdot 120 \]

   if 3.94999999999999981e30 < y

   1. Initial program 97.9%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in x around 0 88.8%

      \[\leadsto \color{blue}{120 \cdot a + -60 \cdot \frac{y}{z - t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+65}:\\ \;\;\;\;\frac{-60}{\frac{z - t}{y}} + a \cdot 120\\ \mathbf{elif}\;y \leq 3.95 \cdot 10^{+30}:\\ \;\;\;\;\frac{60}{z - t} \cdot x + a \cdot 120\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120 + -60 \cdot \frac{y}{z - t}\\ \end{array} \]

Alternative 13: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60}{z - t} \cdot \left(x - y\right) + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (* (/ 60.0 (- z t)) (- x y)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return ((60.0 / (z - t)) * (x - y)) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((60.0d0 / (z - t)) * (x - y)) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return ((60.0 / (z - t)) * (x - y)) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return ((60.0 / (z - t)) * (x - y)) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(60.0 / Float64(z - t)) * Float64(x - y)) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((60.0 / (z - t)) * (x - y)) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(N[(60.0 / N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. associate-/l* 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
4. Step-by-step derivation

   1. associate-/r/ 99.8%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

5. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

6. Final simplification 99.8%

   \[\leadsto \frac{60}{z - t} \cdot \left(x - y\right) + a \cdot 120 \]

Alternative 14: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60}{\frac{z - t}{x - y}} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (60.0d0 / ((z - t) / (x - y))) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(60.0 / Float64(Float64(z - t) / Float64(x - y))) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (60.0 / ((z - t) / (x - y))) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. associate-/l* 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

4. Final simplification 99.8%

   \[\leadsto \frac{60}{\frac{z - t}{x - y}} + a \cdot 120 \]

Alternative 15: 51.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+220}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -9.5e+220) (* -60.0 (/ x t)) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -9.5e+220) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-9.5d+220)) then
        tmp = (-60.0d0) * (x / t)
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -9.5e+220) {
		tmp = -60.0 * (x / t);
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -9.5e+220:
		tmp = -60.0 * (x / t)
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -9.5e+220)
		tmp = Float64(-60.0 * Float64(x / t));
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -9.5e+220)
		tmp = -60.0 * (x / t);
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -9.5e+220], N[(-60.0 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000084e220

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/r/ 99.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   6. Taylor expanded in x around inf 70.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]
   7. Step-by-step derivation

      1. associate-*r/ 70.7%

         \[\leadsto \color{blue}{\frac{60 \cdot x}{z - t}} \]

      2. *-commutative 70.7%

         \[\leadsto \frac{\color{blue}{x \cdot 60}}{z - t} \]

   8. Simplified 70.7%

      \[\leadsto \color{blue}{\frac{x \cdot 60}{z - t}} \]

   9. Taylor expanded in z around 0 58.4%

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t}} \]

   if -9.50000000000000084e220 < x

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 55.1%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+220}:\\ \;\;\;\;-60 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 16: 51.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+221}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.4e+221) (/ (* x -60.0) t) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.4e+221) {
		tmp = (x * -60.0) / t;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.4d+221)) then
        tmp = (x * (-60.0d0)) / t
    else
        tmp = a * 120.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.4e+221) {
		tmp = (x * -60.0) / t;
	} else {
		tmp = a * 120.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.4e+221:
		tmp = (x * -60.0) / t
	else:
		tmp = a * 120.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.4e+221)
		tmp = Float64(Float64(x * -60.0) / t);
	else
		tmp = Float64(a * 120.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.4e+221)
		tmp = (x * -60.0) / t;
	else
		tmp = a * 120.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.4e+221], N[(N[(x * -60.0), $MachinePrecision] / t), $MachinePrecision], N[(a * 120.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.39999999999999994e221

   1. Initial program 99.7%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]
   4. Step-by-step derivation

      1. associate-/r/ 99.7%

         \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)} + a \cdot 120 \]

   6. Taylor expanded in x around inf 70.6%

      \[\leadsto \color{blue}{60 \cdot \frac{x}{z - t}} \]

   7. Taylor expanded in z around 0 58.4%

      \[\leadsto \color{blue}{-60 \cdot \frac{x}{t}} \]
   8. Step-by-step derivation

      1. associate-*r/ 58.5%

         \[\leadsto \color{blue}{\frac{-60 \cdot x}{t}} \]

   9. Simplified 58.5%

      \[\leadsto \color{blue}{\frac{-60 \cdot x}{t}} \]

   if -1.39999999999999994e221 < x

   1. Initial program 99.4%

      \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

   4. Taylor expanded in z around inf 55.1%

      \[\leadsto \color{blue}{120 \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+221}:\\ \;\;\;\;\frac{x \cdot -60}{t}\\ \mathbf{else}:\\ \;\;\;\;a \cdot 120\\ \end{array} \]

Alternative 17: 50.0% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (* a 120.0))

C

double code(double x, double y, double z, double t, double a) {
	return a * 120.0;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = a * 120.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return a * 120.0;
}

Python

def code(x, y, z, t, a):
	return a * 120.0

Julia

function code(x, y, z, t, a)
	return Float64(a * 120.0)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = a * 120.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(a * 120.0), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120 \]
2. Step-by-step derivation

   1. associate-/l* 99.8%

      \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}}} + a \cdot 120 \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\frac{60}{\frac{z - t}{x - y}} + a \cdot 120} \]

4. Taylor expanded in z around inf 53.1%

   \[\leadsto \color{blue}{120 \cdot a} \]

5. Final simplification 53.1%

   \[\leadsto a \cdot 120 \]

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{60}{\frac{z - t}{x - y}} + a \cdot 120 \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0)))

C

double code(double x, double y, double z, double t, double a) {
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0);
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (60.0d0 / ((z - t) / (x - y))) + (a * 120.0d0)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0);
}

Python

def code(x, y, z, t, a):
	return (60.0 / ((z - t) / (x - y))) + (a * 120.0)

Julia

function code(x, y, z, t, a)
	return Float64(Float64(60.0 / Float64(Float64(z - t) / Float64(x - y))) + Float64(a * 120.0))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = (60.0 / ((z - t) / (x - y))) + (a * 120.0);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(60.0 / N[(N[(z - t), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * 120.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023202 
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (+ (/ 60.0 (/ (- z t) (- x y))) (* a 120.0))

  (+ (/ (* 60.0 (- x y)) (- z t)) (* a 120.0)))